Taiwanese Journal of Mathematics

Some New Families of Generalized Euler and Genocchi Polynomials

H. M. Srivastava, Mridula Garg, and Sangeeta Choudhary

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Abstract

The main object of this paper is to introduce and investigate a new generalization of the family of Euler polynomials by means of a suitable generating function. We establish several interesting properties of these general polynomials and derive explicit representations for them in terms of a certain generalized Hurwitz-Lerch Zeta function and in series involving the familiar Gaussian hypergeometric function. Finally, we propose an analogous generalization of the closely-related Genocchi polynomials and show how we can fruifully exploit some potentially useful linear connections of all these three important families of generalized Bernoulli, Euler and Genocchi polynomials with one another.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 283-305.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406175

Digital Object Identifier
doi:10.11650/twjm/1500406175

Mathematical Reviews number (MathSciNet)
MR2780285

Zentralblatt MATH identifier
1262.11040

Subjects
Primary: 11B68: Bernoulli and Euler numbers and polynomials
Secondary: 11B73: Bell and Stirling numbers 33C05: Classical hypergeometric functions, $_2F_1$

Keywords
Bernoulli polynomials Euler polynomials Genocchi polynomials Apostol-Bernoulli polynomials Apostol-Euler polynomials Apostol-Genocchi polynomials Hurwitz-Lerch Zeta function Gaussian hypergeometric function Stirling numbers of the second kind Taylor-Maclaurin series expansion Leibniz rule Pfaff-Kummer transformation Gauss summation theorem

Citation

Srivastava, H. M.; Garg, Mridula; Choudhary, Sangeeta. Some New Families of Generalized Euler and Genocchi Polynomials. Taiwanese J. Math. 15 (2011), no. 1, 283--305. doi:10.11650/twjm/1500406175. https://projecteuclid.org/euclid.twjm/1500406175


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